Simultaneous determination of source term and the initial value in the space-fractional diffusion problem by a novel modified quasi-reversibility regularization method

Abstract

This paper deals with an inverse problem of determining source term and initial data simultaneously for a space-fractional diffusion equation in a strip domain, with the aid of extra measurement data at a fixed time. The uniqueness results are obtained by a simple trick based on the linear property of the proposed equation. Since this problem is ill-posed, a modified quasi-reversibility method is obtained by employing the Fourier transform. Error estimates for source term and initial value are obtained from a suitable parameter choice rule. Finally, several numerical examples show that the proposed regularization method is effective and stable.

Simultaneous Inversion of the Source Term and Initial Value of the Time Fractional Diffusion Equation

“…The topic of simultaneous identification of source item and initial value has been preliminarily studied. Jin [18] et al used a novel modified quasi-reversibility regularization method to identify the source term and initial value of the spatial fractional diffusion equation. Qiu [9] and Jin [17,19] et al studied the simultaneous identification of source terms and initial values of heat equation.…”